Question

Lengths of diagonals of a rhombus ABCD are 16cm and 12cm. Find the side and perimeter of the rhombus

Answer 1

Answer:

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Ans.:- 10cm each side and peri. is 40cm

Step-by-step explanation:

1st diagonal-16cm

2nd diagonal-12cm

Diagonals of rhombus bisect each other at 90°.

1/2 of 1st diagonal- 8cm

1/2 of 2nd diagonal- 6cm

In the given figure ABCD,

Triangle AOB and Triangle COD is formed where,

AO=8 cm, BO=6cm

CO=8cm, DO=6cm

ANGLE AOB=90°

ANGLE COD=90°

Pythagoras' theorem==

$a {}^{2} + b {}^{2} = c {}^{2}$

$6 {}^{2} + 8 {}^{2} = c {}^{2}$

=36+64=100

$c = \sqrt{100}$

c=10cm

hypotenuse =10cm

All sides of a rhombus are equal.

1 side= 10cm

2 side= 10cm

3 side= 10cm

4 side= 10cm

Perimeter of rhombus = 4×s

=> 40cm

Answer 2

Question:-

The lengths of the diagonals of a rhombus are 16cm and 12cm. then find the length of the side of rhombus

Solution:-

we know that diagonal of rhombus,bisect each other in right angle ( 90° ).

we also know that all sides of rhombus are equal ( of equal length ).

so, now

Let rhombus is ABCD and

Diagonal of rhombus are

BD = 16 cm and AC = 12 cm

means,

OD = 8 cm and AO = 6 cm

By pythagorus theorem

To find length of AD ( and all side of rhombus )

=> (AD)² = (OD)² + (AO)²

=> (AD)² = (8)² + (6)²

=> (AD)² = 64 + 36

=> (AD)² = 100

=> AD = √100

=> AD = 10 cm

=>Perimeter of rhombus = 4 × ( side )

=>Perimeter of rhombus = 4 × 10

=>Perimeter of rhombus = 40 cm

Hence length of all side of rhombus is 10 cm and perimeter of rhombus is 40 cm.

i hope it helps you.